Deep neural network using trainable activation functions

This paper proposes trainable activation functions for deep neural network (DNN). A DNN is a feed-forward neural network composed of more than one hidden nonlinear layer. It is characterized by a set of weight matrices, bias vectors, and a nonlinear activation function. In model parameter training, weight matrices and bias vectors are updated using an error back-propagation algorithm but activation functions is not. It is just fixed empirically. Many rectifier-type nonlinear functions have been proposed as activation functions, but the best nonlinear functions for any given task domain remain unknown. In order to address the issue, we propose a trainable activation function. In the proposed approach, conventional nonlinear activation functions were approximated for a Taylor series, and the coefficients were retrained simultaneously with other parameters. The effectiveness of the proposed approach was evaluated for MNIST handwritten digit recognition domain.